Is this derivation correct?

1. The problem statement, all variables and given/known data
For my math homework I have to derivate a complex function.
I think I have come to a solution I just need your help in determine if it is correct.

2. Relevant equations

(lnx)' = 1/x
lnx[tex]^{}x[/tex]=xlnx

3. The attempt at a solution

I will attach a procedure I made in doc and jpeg file so, please read it and tell me if it is correct. Thank you in advance.